Alpha is the portion of an investment’s return that a chosen risk model does not explain. Positive alpha indicates outperformance relative to that model; negative alpha indicates underperformance. It is more specific than simply earning a profit or beating an index without adjusting for risk.
Measuring risk-adjusted performance
Under the capital asset pricing model, Jensen’s alpha equals portfolio return minus [risk-free return + beta × (benchmark return − risk-free return)]. Beta represents sensitivity to the benchmark.
For a simplified one-year example, suppose the portfolio returns 14%, the benchmark 10%, the risk-free return is 2%, and beta is 1.2. The model-implied return is 11.6%, giving alpha of 2.4 percentage points. These figures exclude fees and taxes and use the same period and currency.
What the result can establish
Alpha depends on the benchmark, risk factors, sample period, and costs included. A positive estimate can reflect skill, luck, or risks omitted from the model; it does not prove repeatable ability or predict future gains.
The separate slang meaning
Crypto communities also call supposedly useful early information “alpha.” This informal use describes a claimed informational advantage, not a calculated return. A tip labelled alpha may be inaccurate, promotional, or already reflected in prices.